A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
Rewrite method for theorem proving in first order theory with equality
Journal of Symbolic Computation
Discriminator varieties and symbolic computation
Journal of Symbolic Computation
Computer algebra handbook
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
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We show that the application of the resolution principle to a set of clauses can be regarded as the construction of a term rewriting system confluent on valid formulas. This result allows the extension of usual properties and methods of equational theories (such as Birkhoff's theorem and the Knuth and Bendix completion algorithm) to quantifier-free first order theories. These results are extended to first order predicate calculus in an equational theory, as studied by Plotkin (1972), Slagle (1974) and Lankford (1975). This paper is a continuation of the work of Hsiang & Dershowitz (1983), who have already shown that rewrite methods can be used in first order predicate calculus. The main difference is the following: Hsiang uses rewrite methods only as a refutational proof technique, the initial set of formulas being unsatisfiable iff the equation TRUE = FALSE is generated by the completion algorithm. We generalise these methods to satisfiable theories; in particular, we show that the concept of confluent rewriting system, which is the main tool for studying equational theories, can be extended to any quantifier-free first order theory. Furthermore, we show that rewrite methods can be used even if formulas are kept in clausal form.